A373392 Inverse binomial transform of A135318.
1, 0, 0, 1, -2, 3, -4, 7, -18, 51, -136, 339, -814, 1935, -4620, 11111, -26842, 64923, -156944, 379067, -915078, 2208711, -5331476, 12870639, -31072754, 75018195, -181113240, 437248771, -1055610782, 2548462143, -6152518684, 14853483127, -35859484938, 86572485771
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (-4,-5,-2,2).
Programs
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Mathematica
LinearRecurrence[{-4, -5, -2, 2}, {1, 0, 0, 1}, 35] (* Amiram Eldar, Jun 09 2024 *) -
PARI
a(n) = ((-([-2,-1;-1, 0]^(n-2))[2, 1]) - 2*((I-1)^(n-4) + (-I-1)^(n-4)))/3; \\ Thomas Scheuerle, Jun 04 2024
Formula
G.f.: (1 + 4*x + 5*x^2 + 3*x^3) / ( (1 + 2*x - x^2) * (1 + 2*x + 2*x^2) ).
E.g.f.: 1/6*exp(-x)*(2*cos(-x) + 4*cosh(sqrt(2)*-x) - 3*sqrt(2)*sinh(sqrt(2)*-x)).
a(n) = -4*a(n-1) - 5*a(n-2) - 2*a(n-3) + 2*a(n-4), for n > 4.